On Two-primary Algebraic K-theory of Quadratic Number Rings with Focus on K2

We give explicit formulas for the 2-rank of the algebraic K-groups of quadratic number rings. A 4-rank formula for K2 of quadratic number rings given in [1] provides further information about the actual group structure. The K2 calculations are based on 2and 4rank formulas for Picard groups of quadratic number fields. These formulas are derived in a completely elementary way from the classical 2-rank formula for the narrow ideal class group of a quadratic number field. We also lift the K2 results to higher algebraic K-groups.